Monte Carlo study of two ions in a Stockmayer solvent

Abstract

Monte Carlo calculations have been made for the solvent-ion forces and energies, and the number and moment distributions of solvent molecules around the ions, for a simple model of a pair of singly charged ions of opposite sign in a polar solvent. The solvent was modelled by 4000 Stockmayer particles in the Monte Carlo cell with reduced dipole moment µ*= 2.186, temperature T*= 1.19 and density ρ*= 0.867 chosen to correspond to liquid acetonitrile. The two ions were modelled by the Lennard-Jones potential plus the electrostatic charge with the same ε and σ as the solvent particles. A series of calculations has been made with the ions at a variety of fixed separations from 1.0σ to 4.0σ. The statistical accuracy of the results was improved by sampling mainly within a spherocylindrical volume around the ions.

The distribution of solvent particles around the ions is presented in the form of contour maps. These show that, as with a single isolated ion, there is a single, tight, well-defined highly-oriented layer of solvent particles around the pair of ions with only a small disturbance to the solvent structure beyond the first layer. The disposition of particles in this first layer varies greatly with the ion separation.

The net force between the two ions is obtained only within rather wide limits, but it does provide useful information on the potential of mean force between near ions. The presence of a “hump” in the graph of 〈F_x〉 as a function of ion separation, observed in the preliminary calculations of McDonald and Rasaiah, is confirmed.